Portfolio risk management in a data-rich environment

Abstract

We study risk assessment using an optimal portfolio in which the weights are functions of latent factors and firm-specific characteristics (hereafter, diffusion index portfolio). The factors are used to summarize the information contained in a large set of economic data and thus reflect the state of the economy. First, we evaluate the performance of the diffusion index portfolio and compare it to both that of a portfolio in which the weights depend only on firm-specific characteristics and an equally weighted portfolio. We then use value-at-risk, expected shortfall, and downside probability to investigate whether the weights-modeling approach, which is based on factor analysis, helps reduce market risk. Our empirical results clearly indicate that using economic factors together with firm-specific characteristics helps protect investors against market risk.

JEL Classification

Notes

Acknowledgments

We thank an anonymous referee and the Co-Editor Markus Schmid for their very helpful comments. We also thank Kenneth French and Mark Watson for making the data available to us. The first author acknowledges financial support from IFM2, Montreal, and the second author acknowledges financial support from the Spanish Ministry of Education through Grants SEJ 2011-0031-001.

This table reports the estimation results of the vector of parameters \(\vartheta \) in Eq. (3). The term “BE to ME Ratio” defines the firm-specific characteristic value-weighted average of ratio of book equity (BE) to market equity (ME). The terms “GSF1”, “GSF2”, “GSF3” define the first 3 factors extracted from the first category of macro variables (Goods and services market), “MF1”, “MF2”, “MF3” define the first 3 factors extracted from the second category of macro variables (Money market), “LF1”,..., “LF7” define the first 7 factors extracted from the third category of macro variables (Labor market), and finally “INF1”,..., “INF5” define the first 5 factors extracted from the fourth category of macro variables (prices)

Table 6

Estimation results for portfolio policy function

Firm-specific characteristics

Economic factors

Parameter estimate

\(p\) Value

Sum BE to sum ME ratio

GSF1

0.2682

0.4382

Sum BE to sum ME ratio

GSF2

1.5929

0.1072

Sum BE to sum ME ratio

GSF3

3.1326

0.0300

Sum BE to sum ME ratio

INF1

-4.6056

0.0001

Sum BE to sum ME ratio

INF2

0.1990

0.4320

Sum BE to sum ME ratio

INF3

-3.7934

0.0015

Sum BE to sum ME ratio

INF4

0.2376

0.4138

Sum BE to sum ME ratio

INF5

0.0193

0.4923

Sum BE to sum ME ratio

LF1

-11.1707

0.0000

Sum BE to sum ME ratio

LF2

9.4580

0.0000

Sum BE to sum ME ratio

LF3

-3.5713

0.0015

Sum BE to sum ME ratio

LF4

3.3845

0.0030

Sum BE to sum ME ratio

LF5

0.7037

0.2799

Sum BE to sum ME ratio

LF6

-5.4889

0.0000

Sum BE to sum ME ratio

LF7

6.0993

0.0000

Sum BE to sum ME ratio

MF1

-3.5528

0.0011

Sum BE to sum ME ratio

MF2

-0.8755

0.3216

Sum BE to sum ME ratio

MF3

0.0543

0.4866

This table reports the estimation results of the vector of parameters \(\vartheta \) in Eq. (). The term “Sum BE to sum ME Ratio” defines the firm-specific characteristic ratio of sum of book equity (BE) to sum of market equity (ME). The terms “GSF1”, “GSF2”, “GSF3” define the first three factors extracted from the first category of macro variables (goods and services market), “MF1”, “MF2”, “MF3” define the first three factors extracted from the second category of macro variables (money market), “LF1”,..., “LF7” define the first seven factors extracted from the third category of macro variables (Labor market), and finally “INF1”,..., “INF5” define the first five factors extracted from the fourth category of macro variables (prices)

Table 7

Estimation results for portfolio policy function

Firm-specific characteristics

Economic factors

Parameter estimate

\(p\) Value

Size

GSF1

-0.6920

0.0008

Size

GSF2

-0.8623

0.0000

Size

GSF3

-0.9582

0.0000

Size

INF1

-0.4347

0.0000

Size

INF2

-0.5064

0.0004

Size

INF3

-0.5914

0.0000

Size

INF4

-0.5862

0.0001

Size

INF5

0.4882

0.0004

Size

LF1

-1.2443

0.0000

Size

LF2

-0.9340

0.0000

Size

LF3

0.5213

0.0002

Size

LF4

-0.7422

0.0000

Size

LF5

0.2675

0.0133

Size

LF6

0.8271

0.0000

Size

LF7

-0.3162

0.0155

Size

MF1

-0.8110

0.0000

Size

MF2

-0.3247

0.0082

Size

MF3

0.3623

0.0006

This table reports the estimation results of the vector of parameters \(\vartheta \) in Eq. (3). The term “Size” defines the firm-specific characteristic average firm size. The terms “GSF1”, “GSF2”, “GSF3” define the first three factors extracted from the first category of macro variables (Goods and services market), “MF1”, “MF2”, “MF3” define the first three factors extracted from the second category of macro variables (money market), “LF1”,..., “LF7” define the first seven factors extracted from the third category of macro variables (labor market), and finally “INF1”,..., “INF5” define the first five factors extracted from the fourth category of macro variables (prices)

Table 8

Estimation results for portfolio policy function

Firm-specific characteristics

Economic factors

Parameter estimate

\(p\) Value

Proportion of firms by the industry

GSF1

60.9533

0.1071

Proportion of firms by the industry

GSF2

40.8455

0.1434

Proportion of firms by the industry

GSF3

292.9891

0.0000

Proportion of firms by the industry

INF1

5.0096

0.4001

Proportion of firms by the industry

INF2

186.7678

0.0000

Proportion of firms by the industry

INF3

-0.6173

0.4880

Proportion of firms by the industry

INF4

153.9121

0.0000

Proportion of firms by the industry

INF5

-112.7446

0.0000

Proportion of firms by the industry

LF1

88.7534

0.0311

Proportion of firms by the industry

LF2

172.0771

0.0000

Proportion of firms by the industry

LF3

211.5271

0.0000

Proportion of firms by the industry

LF4

208.2252

0.0000

Proportion of firms by the industry

LF5

30.1998

0.1424

Proportion of firms by the industry

LF6

-272.3654

0.0000

Proportion of firms by the industry

LF7

176.1424

0.0000

Proportion of firms by the industry

MF1

141.4166

0.0000

Proportion of firms by the industry

MF2

-78.9428

0.0021

Proportion of firms by the industry

MF3

-49.4723

0.0216

This table reports the estimation results of the vector of parameters \(\vartheta \) in Eq. (3). The term “Proportion of firms by the industry” defines the firm-specific characteristic proportion of firms by industry. The terms “GSF1”, “GSF2”, “GSF3” define the first three factors extracted from the first category of macro variables (goods and services market), “MF1”, “MF2”, “MF3” define the first three factors extracted from the second category of macro variables (money market), “LF1”,..., “LF7” define the first seven factors extracted from the third category of macro variables (labor market), and finally “INF1”,..., “INF5” define the first five factors extracted from the fourth category of macro variables (prices)

Table 9

This table shows the descriptive statistics that correspond to an out-of-sample prediction of DFI, IC, and EW portfolio returns

DFI portfolio

IC portfolio

EW portfolio

Mean

0.0139

0.0093

0.0087

SD

0.0677

0.0223

0.0415

Skewness

0.4679

0.0648

-1.1857

Kurtosis

6.3369

6.7066

7.2649

Table 10

This table reports the sharpe ratio (SR), (Sharpe 1966), and the FT ratios, (Farinelli and Tibiletti 2008), that correspond to an out-of-sample prediction of DFI, IC, and EW portfolio returns

DFI portfolio

IC portfolio

EW portfolio

SR\((\omega ) \)

\(0.2050\)

\(0.4182\)

\(0.2102\)

FT\(_{(p=q=1,b=0)}\)

\(1.4160\)

\(1.4201\)

\(0.9762\)

FT\(_{(p=1,q=2,b=0)}\)

\(0.9533\)

\(0.8583\)

\(0.6706\)

FT\(_{(p=1,q=3,b=0)}\)

\(0.7092\)

\(0.6247\)

\(0.4988\)

FT \(_{(p=1,q=4,b=0)}\)

\(0.5714\)

\(0.5060\)

\(0.4009\)

Table 11

This table shows the average of portfolio weights in low and high portfolio return statistics (mean, standard-deviation, skewness) that correspond to an out-of-sample prediction of DFI, IC, and EW portfolio returns